Hitherto in solid state imaging, images have conventionally been reconstructed from profiles using back projection algorithms. The essence of back projection is the use of just one magnetic field gradient in the profile direction. A common way to obtain a profile is to record the free induction decay signal or echo as a function of time in the presence of a gradient which is linear in space and then to Fourier transform the decay signal or echo. This procedure is commonly known as frequency encoding. The gradient is rotated and the experiment repeated until sufficient profiles are available for an image to be constructed using back projection algorithms. In the (reciprocal) k-space description of NMR imaging which has now been widely adopted as the means of describing NMR imaging techniques, data is recorded radially outwards from the centre of k-space. An alternative to frequency encoding is phase encoding, where the angle through which a spin precesses during a fixed encoding time is recorded as a function of gradient strength. A useful review paper on back projection techniques has been written by P. Mansfield and is entitled "Imaging by Nuclear Magnetic Resonance" (J. Phys. E. Sci. Instrum., 21 (1988) 18-30).
Although back projection methods have been conventionally used in solid state NMR imaging, it would be advantageous to use two dimensional Fourier transform (2DFT) techniques since these might be expected to lead to an improvement in image quality. 2DFT techniques have been used with great success in liquid state NMR imaging (see, for example, the paper by A. Kumar, D. Welti and R. R. Ernst in J. Magn. Reson. 18 (1975) 69).
The essence of such 2DFT techniques is a period of phase (or less often frequency) encoding in one direction followed immediately by a period of frequency encoding in an orthogonal direction during which the data is read out. The experiment is repeated for incremented values of the phase gradient. k-space is sampled on a rectilinear grid of points allowing reconstruction of the image by two dimensional Fourier Transformation. The improvement in image quality for liquid state NHR imaging has been found to be substantial, partly because k-space is covered more uniformly and partly because the image reconstruction is far less susceptible to artifacts and noise tn the data set. In particular star and streak artifacts common in back projection are largely eliminated.
2DFT methods are in general more experimentally complex than back projection methods, because during the course of one free induction decay the phase encode gradient has to be switched off, to be replaced by the frequency encode gradient. For back projection methods, a single frequency encode gradient on throughout the experiment is sufficient. One problem associated particularly with the NHR imaging of the solid state using 2DFT methods is that it is difficult to switch magnetic field gradients sufficiently rapidly to avoid losing useful imaging information. This problem arises from the short spin-spin relaxation times (T.sub.2) usually associated with the solid state, which force the use of short encoding times. Not surprisingly this has limited the use of 2DFT methods whilst favouring the development of back projection methods.
An attempt to develop solid state imaging experiments using 2DFT methods has been made by Chingas et al. (J. Hagn. Reson. 66(1986) 530). A line narrowing sequence was used to hold up the magnetisation whilst first a static phase encoding gradient and then a static frequency encoding gradient was applied. In order to avoid artifacts accumulating during the period in which the gradients were switched over, the magnetisation was stored along a magic angle direction by the introduction of appropriate storage and retrieval rf pulses before and after the changeover. In principle this is a good procedure which can additionally provide an image contrast mechanism. However it requires considerable experimental skill to set it up accurately, especially as the storage and retrieval pulses in the experiment of Chingas et al. were .pi./4 rather than .pi./2 rotations.